Fast List Decoders for Polarization-Adjusted Convolutional (PAC) Codes

TL;DR

This paper introduces fast list decoding algorithms for PAC codes, significantly reducing decoding latency while maintaining error-correction performance, thus making PAC codes more practical for real-time applications.

Contribution

The paper proposes four types of constituent nodes and corresponding fast list decoding algorithms that cut decoding time by over 50% without sacrificing performance.

Findings

Fast list decoding reduces decoding time by over 50%.

Three node types achieve same error correction as traditional list decoding.

Four node types further decrease latency with negligible performance loss.

Abstract

A latest coding scheme named polarization-adjusted convolutional (PAC) codes is shown to approach the dispersion bound for the code (128,64) under list decoding. However, to achieve the near-bound performance, the list size of list decoding needs to be excessively large, which leads to insufferable latency. In this paper, to improve the speed of list decoding, fast list decoders for PAC codes are proposed. We define four types of constituent nodes and provide fast list decoding algorithms for each of them. Simulation results present that fast list decoding with three types of constituent nodes can yield exactly the same error-correction performance as list decoding, and reduce more than 50% time steps for the code (128,64). Moreover, fast list decoding with four types of constituent nodes can further reduce decoding latency with negligible performance degradation.